This arrangement enables the computer to examine any sin which he wishes to extract, so as to guard against any typographical error; and, if the table of the multiples of 2 verl' were appended, to check readily the computation itself. When, however, the differences have only a few figures, the ordinary method, of placing them in separate columns, is to be preferred; it saves room, while the practised calculator has no difficulty in performing the requisite additions or subtractions. The utility of this arrangement has been long recognised.

In the case of tables for common use, which are, in general, abbreviations of original calculations to a greater number of places, it is enough to give the first differences when these vary much.

When such means of verification have been provided, the user of the table can make sure that the number which he extracts contains no error; and if all users were to habitually make this examination, printed tables, and above all those printed from stereotype, would be gradually freed from errors of press.

4. On an Unnamed Palæozoic Annelid. By Professor Duns. (Plate IV.)

CYMADERMA (nov. gen.).-Generis Characteres:-Corpus cylindricum, elongatum, nudum, striatum; striæ tenues, in ordinem undi datæ, et ubique corpus cingentes, ita ut cutis subrugosa videatur; linea dor sualis continua, alternasque cavaturas ovatus et vertices ostendens; nulla verorum articulamentorum indicia; vestigium tortuosum, bisulcum.

CYMADERMA (new genus).—Generic Characters:-Body cylindrical, elongated, naked, striated; striæ minute, waved symmetrically, encompassing the form in all parts, and giving to the skin a subrugose appearance; a continuous dorsal line, showing alternate oval depressions and slight ridges; no traces of true articulations; track, tortuous bisulcate.

This annuloid fossil was obtained from upper Carboniferous strata, in a cutting on the Midland Railway, valley of the Ribble, near Settle, Yorkshire. Peculiarities characteristic of the striation and the median dorsal line led me to conclude that the form was probably rare, or one that had not been described. It was thus of importance to get the other part of the slab on which the impres

* Etymol. kuua, unda, dépμa, cutis.

sion, or intaglio, corresponding to the rounded relief, might be expected. The friend who had forwarded the fossil made diligent search, but found the upper part of the slab had been destroyed. In answer to a request for any animal tracks, or traces of organisms that might be met with in the same, or closely related deposits, he sent me several slabs of compact dark-coloured micaceous, sandy shale, on which some markings occurred. On splitting these, they were found crowded with tracks and casts of forms closely resembling that first sent, though the matrix is lithologically different. These shales intervene between bands of the so-called gritstone, in which the form now noticed was found. Its position was about 16 feet from the surface, in a gritstone bed 4 feet thick, having above a deposit of alternating shales and gritstones nearly 15 feet thick and below a bed of limestone.

The dark-coloured slabs present features of much interest. They contain traces of three species, the prevailing one being identical with that now before us, though none of the characteristic marks are so sharply outlined. They make it clear, however, that the surface on which the median line occurs is dorsal, and they establish the bisulcate character of the track. On the reverse of one slab, the intaglio I was anxious to obtain shows distinctly that the dorsal line is ridged. This is also very well marked in another. In both the slight dorsal ridge is represented by a corresponding depression or furrow in the overlying shale. Even the outlines of these tracks are suggestive to the ichnologist. Some of them are comparatively deep, some shallow; in some the bisulcate character is well seen, while in others the lower surface of the track is flat. The explanation of this is obvious. If, for example, we look at the tracks, say, of our common whelks (Littorina), we see that those formed in shallow shore-pools are flat; those on very wet sand are slightly hollow, their edges presenting a corrugated appearance; while those made on fine sand beginning to dry, are marked at regular intervals with distinct transverse lines. It is not unusual to observe all these crossing one another, or seeming to form loops with each other. The waved whelk (Buccinum undatem) makes a bisulcate track on the sand when it is partially dry. Occasionally, however, it trails the sharp edge of its operculum in such a way as to give three sulci. Ichnologists may thus have the track of only

one form before them, when they describe three or four apparently different ones, and trace them to different species. Thus, such terms as unisulcus, bisulcus, trisulcus, unisulcus corrugatus, and the like, instead of indicating so many distinct species, may, in reality, express the varying form of the track of one only. Perhaps, even the Hitchcocks' in their magnificent works on ichnology have not given due weight to this consideration.*

The slabs laid on the table have been examined with great care, in the hope of detecting traces of hairs, setæ, or any other characteristic marks of true recent annelids. But neither hairs nor bristles have been found. On most of the slabs, however, markings occur, which I am inclined to regard as the outlines of organs analogous to the gill-leaves of such forms as Phyllodoce. These are worthy the attention of naturalists. They are numerous, and have not, I think, been observed before. While occurring on the same surface as the outlines and tracks of the organisms, only in one instance they seem attached to them, but even in this case the association is doubtful. See Plate IV. fig. 2, for an outline of some of these markings. In one case, in which a good duplicate was obtained, distinct traces as of a fringe appear. An enlarged rough outline of part of this fringe is shown on the Plate, IV. fig. 4. On the same specimen a good many annulate pointed objects occur, two of which are represented at a and b fig. 2.

There can be no doubt that both tube inhabiting and errant Annelida existed in paleozoic time-traces of some being found even in the Laurentian rocks-though little is known of their true nature and relations. The genera conchiolites, cornulites, serpulites, spirorbis, and trachyderma, may be said to complete the list of the former, and the genera arenicolites, crossopodia, myrianites, and nereites that of the latter. But even some of these generic designations are open to criticism, or cumbered with doubt, and it is questionable if, in any of these cases, we have a true representation of the animal itself. Such considerations add to the value of the specimen now under notice. It has no resemblance to any of the forms just named. The first examples on record having some

"Ichnology of Massachusetts." By Edward Hitchcock, Boston, 1858. Supplement to the Ichnology of New England." Edited by C. H. Hitchcock, Boston, 1865.